Basic Math Examples

$\frac{2^{- 3} a^{\frac{2}{3}} b^{4}}{2^{- 2} a^{\frac{1}{6}} b^{4}}$

Step 1

Move $2^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{a^{\frac{2}{3}} b^{4}}{2^{- 2} a^{\frac{1}{6}} b^{4} \cdot 2^{3}}$

Step 2

Simplify the denominator.

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Step 2.1

Multiply $2^{- 2}$ by $2^{3}$ by adding the exponents.

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Step 2.1.1

Move $2^{3}$ .

$\frac{a^{\frac{2}{3}} b^{4}}{2^{3} \cdot 2^{- 2} a^{\frac{1}{6}} b^{4}}$

Step 2.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{a^{\frac{2}{3}} b^{4}}{2^{3 - 2} a^{\frac{1}{6}} b^{4}}$

Step 2.1.3

Subtract $2$ from $3$ .

$\frac{a^{\frac{2}{3}} b^{4}}{2^{1} a^{\frac{1}{6}} b^{4}}$

Step 2.2

Simplify $2^{1} a^{\frac{1}{6}} b^{4}$ .

$\frac{a^{\frac{2}{3}} b^{4}}{2 a^{\frac{1}{6}} b^{4}}$

Step 3

Move $a^{\frac{1}{6}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$\frac{a^{\frac{2}{3}} b^{4} a^{- \frac{1}{6}}}{2 b^{4}}$

Step 4

Multiply $a^{\frac{2}{3}}$ by $a^{- \frac{1}{6}}$ by adding the exponents.

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Step 4.1

Move $a^{- \frac{1}{6}}$ .

$\frac{a^{- \frac{1}{6}} a^{\frac{2}{3}} b^{4}}{2 b^{4}}$

Step 4.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{a^{- \frac{1}{6} + \frac{2}{3}} b^{4}}{2 b^{4}}$

Step 4.3

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{a^{- \frac{1}{6} + \frac{2}{3} \cdot \frac{2}{2}} b^{4}}{2 b^{4}}$

Step 4.4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.4.1

Multiply $\frac{2}{3}$ by $\frac{2}{2}$ .

$\frac{a^{- \frac{1}{6} + \frac{2 \cdot 2}{3 \cdot 2}} b^{4}}{2 b^{4}}$

Step 4.4.2

Multiply $3$ by $2$ .

$\frac{a^{- \frac{1}{6} + \frac{2 \cdot 2}{6}} b^{4}}{2 b^{4}}$

Step 4.5

Combine the numerators over the common denominator.

$\frac{a^{\frac{- 1 + 2 \cdot 2}{6}} b^{4}}{2 b^{4}}$

Step 4.6

Simplify the numerator.

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Step 4.6.1

Multiply $2$ by $2$ .

$\frac{a^{\frac{- 1 + 4}{6}} b^{4}}{2 b^{4}}$

Step 4.6.2

Add $- 1$ and $4$ .

$\frac{a^{\frac{3}{6}} b^{4}}{2 b^{4}}$

Step 4.7

Cancel the common factor of $3$ and $6$ .

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Step 4.7.1

Factor $3$ out of $3$ .

$\frac{a^{\frac{3 (1)}{6}} b^{4}}{2 b^{4}}$

Step 4.7.2

Cancel the common factors.

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Step 4.7.2.1

Factor $3$ out of $6$ .

$\frac{a^{\frac{3 \cdot 1}{3 \cdot 2}} b^{4}}{2 b^{4}}$

Step 4.7.2.2

Cancel the common factor.

$\frac{a^{\frac{3 \cdot 1}{3 \cdot 2}} b^{4}}{2 b^{4}}$

Step 4.7.2.3

Rewrite the expression.

$\frac{a^{\frac{1}{2}} b^{4}}{2 b^{4}}$

Step 5

Cancel the common factor.

$\frac{a^{\frac{1}{2}} b^{4}}{2 b^{4}}$

Step 6

Rewrite the expression.

$\frac{a^{\frac{1}{2}}}{2}$